Transverse Instability of Rogue Waves

TL;DR

This paper investigates the transverse stability of rogue wave solutions in the 2+1 hyperbolic nonlinear Schrödinger equation, revealing significant transverse instability and emphasizing the importance of considering transverse dimensions in rogue wave studies.

Contribution

It demonstrates the transverse instability of rogue wave solutions in 2+1 dimensions and links the stability of the Peregrine soliton to that of the background wave.

Findings

Rogue wave solutions exhibit strong transverse instability.

The Peregrine soliton's stability matches that of the background wave.

Transverse dimensions are crucial in rogue wave analysis.

Abstract

Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Schr\"odinger equation is often used to model rogue waves; it is an envelope description of plane waves and admits the so-called Pergerine and Kuznetov-Ma soliton solutions. However, in deep water waves and certain electromagnetic systems where there are two significant transverse dimensions, the 2+1 hyperbolic nonlinear Schrodinger equation is the appropriate wave envelope description. Here we show that these rogue wave solutions suffer from strong transverse instability at long and short frequencies. Moreover, the stability of the Peregrine soliton is found to coincide with that of the background plane wave. These results indicate that, when applicable, transverse dimensions must be taken into account when investigating rogue wave pheneomena.